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Add a non-recursive version of BetaAdicMonoid.relations_automaton and…
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… correct some bugs.
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Paul MERCAT authored and Paul MERCAT committed Apr 4, 2014
1 parent e99d542 commit cf8e9c8
Showing 1 changed file with 175 additions and 13 deletions.
188 changes: 175 additions & 13 deletions src/sage/monoids/beta_adic_monoid.pyx
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Expand Up @@ -438,16 +438,16 @@ class BetaAdicMonoid(Monoid_class):

return G

def _relations_automaton_rec (self, current_state, di, parch, pultra, m, Cd, ext, verb=False):
def _relations_automaton_rec (self, current_state, di, parch, pultra, m, Cd, ext, verb=False, niter=-1):
r"""
Used by relations_automaton()
"""

if verb and count%10000 == 0: print count
#current_state
if niter == 0:
return di

global count
#print count
if verb and count%10000 == 0: print count
if count == 0:
return di
count -= 1
Expand Down Expand Up @@ -481,13 +481,13 @@ class BetaAdicMonoid(Monoid_class):
if ok:
#on ajoute l'état et la transition à l'automate
di[current_state][e] = c
di = self._relations_automaton_rec (current_state=e, di=di, parch=parch, pultra=pultra, m=m, Cd=Cd, ext=ext, verb=verb)
di = self._relations_automaton_rec (current_state=e, di=di, parch=parch, pultra=pultra, m=m, Cd=Cd, ext=ext, verb=verb, niter=niter-1)
else:
#ajoute la transition
di[current_state][e] = c
return di

def relations_automaton (self, ext=False, ss=None, noss=False, verb=False, step=100, limit=None):
def relations_automaton (self, ext=False, ss=None, noss=False, verb=False, step=100, limit=None, niter=None):
r"""
Compute the relations automaton of the beta-adic monoid (with or without subshift).
See http://www.latp.univ-mrs.fr/~paul.mercat/Publis/Semi-groupes%20fortement%20automatiques.pdf for a definition of such automaton (without subshift).
Expand All @@ -505,9 +505,7 @@ class BetaAdicMonoid(Monoid_class):
- ``verb`` - bool (default: ``False``)
If True, print informations for debugging.
- ``prec`` - precision of returned values (default: ``53``)
- ``step`` - int (default: ``100``)
Stop to an intermediate state of the computing to verify that all is right.
Expand Down Expand Up @@ -642,9 +640,11 @@ class BetaAdicMonoid(Monoid_class):
count = -1
else:
count = limit
if niter is None:
niter = -1
#print count
if verb: print "Parcours..."
di = self._relations_automaton_rec (current_state=K.zero(), di=dict([]), parch=parch, pultra=pultra, m=m, Cd=Cd, ext=ext, verb=verb)
di = self._relations_automaton_rec (current_state=K.zero(), di=dict([]), parch=parch, pultra=pultra, m=m, Cd=Cd, ext=ext, verb=verb, niter=niter)

if count == 0:
print "Nombre max d'états atteint."
Expand Down Expand Up @@ -675,6 +675,162 @@ class BetaAdicMonoid(Monoid_class):
res.F = res.vertices()
return res

def relations_automaton2 (self, verb=False, step=100, limit=None, niter=None):
r"""
Do the same as relations_automaton, but avoid recursivity in order to avoid the crash of sage.
INPUT:
- ``verb`` - bool (default: ``False``)
If True, print informations for debugging.
- ``step`` - int (default: ``100``)
Stop to an intermediate state of the computing to verify that all is right.
- ``limit``- int (default: None)
Stop the computing after a number of states limit.
OUTPUT:
A Automaton.
"""

K = self.C[0].parent()
b = self.b

if verb: print K

#détermine les places qu'il faut considérer
parch = []
for p in K.places(): #places archimédiennes
if p(b).abs() < 1:
parch += [p]
pi = K.defining_polynomial()
from sage.rings.arith import gcd
pi = pi/gcd(pi.list()) #rend le polynôme à coefficients entiers et de contenu 1
lp = (Integer(pi.list()[0])).prime_divisors() #liste des nombres premiers concernés
pultra = [] #liste des places ultramétriques considérées
for p in lp:
#détermine toutes les places au dessus de p dans le corps de nombres K
k = Qp(p)
Kp = k['a']
a = Kp.gen()
for f in pi(a).factor():
kp = f[0].root_field('e')
if kp == k:
c = f[0].roots(kp)[0][0]
else:
c = kp.gen()
if verb: print "c=%s (abs=%s)"%(c, (c.norm().abs())**(1/f[0].degree()))
if (c.norm().abs())**(1/f[0].degree()) < 1: #absp(c, c, f[0].degree()) > 1:
pultra += [(c, f[0].degree())]

if verb: print "places: "; print parch; print pultra

#calcule les bornes max pour chaque valeur absolue
Cd = Set([c-c2 for c in self.C for c2 in self.C])
if verb: print "Cd = %s"%Cd
m = dict([])
for p in parch:
m[p] = max([p(c).abs() for c in Cd])/abs(1-p(p.domain().gen()).abs())
for p, d in pultra:
m[p] = max([absp(c, p, d) for c in Cd])

if verb: print "m = %s"%m

if verb: print K.zero().parent()

if limit is None:
count = -1
else:
count = limit
if niter is None:
niter = -1

if verb: print "Parcours..."

di=dict([])
S = [K.zero()] #set of states to look at
iter = 0
while len(S) != 0:
if iter == niter:
break
for s in S:
S.remove(s)
if not di.has_key(s):
di[s] = dict([])
if count%10000 == 0:
print count
count-=1
if count == 0:
iter = niter-1 #to break the main loop
break
for c in Cd: #parcours les transitions partant de current_state
e = (s + c)/b #calcule l'état obtenu en suivant la transition c
#if verb: print "b=%s, e=%s, cur=%s, c=%s, di=%s"%(b, e, current_state, c, di)
if not di.has_key(e): #détermine si l'état est déjà dans le dictionnaire
ok = True
#calcule les valeurs abolues pour déterminer si l'état n'est pas trop grand
for p in parch:
if p(e).abs() >= m[p]:
ok = False
break
if not ok:
continue #cesse de considérer cette transition
for p, d in pultra:
if absp(e, p, d) > m[p]:
#if verb: print "abs(%s)=%s trop grand !"%(e, absp(e, p, d))
ok = False
break
if ok:
#on ajoute l'état et la transition à l'automate
di[s][e] = c
S.append(e)
else:
#ajoute la transition
di[s][e] = c
iter+=1

if count == 0:
print "Nombre max d'états atteint."
return
else:
if verb:
if limit is None:
print "%s états parcourus."%(-1-count)
else:
print "%s états parcourus."%(limit-count)

res = Automaton(di, loops=True) #, multiedges=True)

if verb: print "Avant emondation : %s"%res

res.I = [K.zero()]
res.A = Set([c-c2 for c in self.C for c2 in self.C])
res.F = [K.zero()]
if verb: print "Emondation..."
res.emonde()
return res

def critical_exponent_aprox (self, niter=10, verb=False):
b = self.b
K = b.parent()
C = self.C
S = set([K.zero()])
for i in range(niter):
S2 = set([])
for s in S:
for c in C:
S2.add((s+c)/b)
#intervertit S et S2
S3 = S2
S2 = S
S = S3
if verb: print len(S)
from sage.functions.log import log
print "%s"%(log(len(S)).n()/(niter*abs(log(abs(b.n())))))

def complexity (self, verb = False):
r"""
Return a estimation of an upper bound of the number of states of the relations automaton.
Expand Down Expand Up @@ -907,7 +1063,7 @@ class BetaAdicMonoid(Monoid_class):
ssd = ssd.emonde0_simplify()
return ssd

def reduced_words_automaton (self, ss=None, Iss=None, ext=False, verb=False, step=None):
def reduced_words_automaton (self, ss=None, Iss=None, ext=False, verb=False, step=None, arel=None):
r"""
Compute the reduced words automaton of the beta-adic monoid (with or without subshift).
See http://www.latp.univ-mrs.fr/~paul.mercat/Publis/Semi-groupes%20fortement%20automatiques.pdf for a definition of such automaton (without subshift).
Expand All @@ -924,12 +1080,15 @@ class BetaAdicMonoid(Monoid_class):
- ``ext`` - bool (default: ``True``)
If True, compute the extended relations automaton (which permit to describe infinite words in the monoid).
- ``verb``- bool (default: ``False``)
- ``verb`` - bool (default: ``False``)
If True, print informations for debugging.
- ``step`` - int (default: ``None``)
Stop to a intermediate state of the computing to make verifications.
- ``arel`` - Automaton (default: ``None``)
Automaton of relations.
OUTPUT:
A Automaton.
Expand Down Expand Up @@ -968,7 +1127,10 @@ class BetaAdicMonoid(Monoid_class):

if verb: print "Calcul de l'automate des relations..."

a = self.relations_automaton(noss=True)
if arel is None:
a = self.relations_automaton(noss=True)
else:
a = arel

if verb: print " -> %s"%a

Expand Down

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